{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple application of ft-fsd-path-planning\n",
    "\n",
    "This notebook shows how to use the ft-fsd-path-planning package to calculate a centerline\n",
    "given the car's position and direction as well as the cone positions (and optionally the colors)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation\n",
    "\n",
    "We will generate a simple track with a constant curvature and a few cones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from fsd_path_planning.utils.math_utils import unit_2d_vector_from_angle, rotate\n",
    "from fsd_path_planning.utils.cone_types import ConeTypes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_inner = np.arange(0, np.pi / 2, np.pi / 15)\n",
    "phi_outer = np.arange(0, np.pi / 2, np.pi / 20)\n",
    "\n",
    "points_inner = unit_2d_vector_from_angle(phi_inner) * 9\n",
    "points_outer = unit_2d_vector_from_angle(phi_outer) * 12\n",
    "\n",
    "center = np.mean((points_inner[:2] + points_outer[:2]) / 2, axis=0)\n",
    "points_inner -= center\n",
    "points_outer -= center\n",
    "\n",
    "rotated_points_inner = rotate(points_inner, -np.pi / 2)\n",
    "rotated_points_outer = rotate(points_outer, -np.pi / 2)\n",
    "cones_left_raw = rotated_points_inner\n",
    "cones_right_raw = rotated_points_outer\n",
    "\n",
    "\n",
    "rng = np.random.default_rng(0)\n",
    "rng.shuffle(cones_left_raw)\n",
    "rng.shuffle(cones_right_raw)\n",
    "\n",
    "\n",
    "car_position = np.array([0.0, 0.0])\n",
    "car_direction = np.array([1.0, 0.0])\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Color information\n",
    "\n",
    "The algorithm can work without knowing the colors of the cones. However, if the colors are known, the algorithm can use them to improve the result. In the following cell we will overwrite the color information of some cones. If you want to keep the color information comment out the relevant lines in the following cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mask_is_left = np.ones(len(cones_left_raw), dtype=bool)\n",
    "mask_is_right = np.ones(len(cones_right_raw), dtype=bool)\n",
    "\n",
    "# for demonstration purposes, we will only keep the color of the first 4 cones\n",
    "# on each side\n",
    "mask_is_left[np.argsort(np.linalg.norm(cones_left_raw, axis=1))[4:]] = False\n",
    "mask_is_right[np.argsort(np.linalg.norm(cones_right_raw, axis=1))[4:]] = False\n",
    "\n",
    "cones_left = cones_left_raw[mask_is_left]\n",
    "cones_right = cones_right_raw[mask_is_right]\n",
    "cones_unknown = np.row_stack(\n",
    "    [cones_left_raw[~mask_is_left], cones_right_raw[~mask_is_right]]\n",
    ")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "\n",
    "The following cell visualizes the track and the cones. The cones are colored according to their color information. If a cone has no color information, it is colored black."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f62506d7a30>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "blue_color = \"#7CB9E8\"\n",
    "yellow_color = \"gold\"\n",
    "\n",
    "plt.scatter(cones_left[:, 0], cones_left[:, 1], c=blue_color, label=\"left\")\n",
    "plt.scatter(cones_right[:, 0], cones_right[:, 1], c=yellow_color, label=\"right\")\n",
    "plt.scatter(cones_unknown[:, 0], cones_unknown[:, 1], c=\"k\", label=\"unknown\")\n",
    "plt.legend()\n",
    "plt.plot(\n",
    "    [car_position[0], car_position[0] + car_direction[0]],\n",
    "    [car_position[1], car_position[1] + car_direction[1]],\n",
    "    c=\"k\",\n",
    ")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Path planning\n",
    "\n",
    "The following cells show how to use the `PathPlanner` class. \n",
    "\n",
    "First we import the class as well as the mission and cone type enums."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fsd_path_planning import PathPlanner, MissionTypes, ConeTypes\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we create an instance of the `PathPlanner` class. The constuctor takes the mission type as an argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "planner = PathPlanner(MissionTypes.trackdrive)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now setup the inputs for the actual path calculation.\n",
    "\n",
    "The cones are given to the path planner as a list of 2D numpy arrays. The list contains five arrays, each representing cones of different colors. See the `ConeTypes` class to see the actual indices of the different cone colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ConeTypes.UNKNOWN = 0\n",
      "ConeTypes.RIGHT = 1\n",
      "ConeTypes.LEFT = 2\n",
      "ConeTypes.START_FINISH_AREA = 3\n",
      "ConeTypes.START_FINISH_LINE = 4\n"
     ]
    }
   ],
   "source": [
    "for i, c in enumerate(ConeTypes):\n",
    "    print(c, f\"= {i}\")\n",
    "\n",
    "cones_by_type = [np.zeros((0, 2)) for _ in range(5)]\n",
    "cones_by_type[ConeTypes.LEFT] = cones_left\n",
    "cones_by_type[ConeTypes.RIGHT] = cones_right\n",
    "cones_by_type[ConeTypes.UNKNOWN] = cones_unknown\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now ready to calculate the path. The `calculate_path_in_global_frame` function receives the car's position and direction as well as the list of 2D numpy arrays containing the cone positions. It returns a 2D numpy array containing the centerline points. The function can optionally return the intermediate results of the algorithm. This is useful for debugging and visualization, which we will do in the following cells."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "out = planner.calculate_path_in_global_frame(\n",
    "    cones_by_type, car_position, car_direction, return_intermediate_results=True\n",
    ")\n",
    "\n",
    "(\n",
    "    path,\n",
    "    sorted_left,\n",
    "    sorted_right,\n",
    "    left_cones_with_virtual,\n",
    "    right_cones_with_virtual,\n",
    "    left_to_right_match,\n",
    "    right_to_left_match,\n",
    ") = out\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# you can uncomment the following line to get an approximate speed profile\n",
    "# %timeit planner.calculate_path_in_global_frame(cones_by_type, car_position, car_direction)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results\n",
    "\n",
    "We can now visualize the calculated path. The path is extrapolated/trimmed so that it has a specified length.\n",
    "\n",
    "In the next cell we will visualize the intermediate results of the algorithm. The intermediate results are returned by the `calculate_path_in_global_frame` function if the `return_intermediate_results` argument is set to `True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(cones_left[:, 0], cones_left[:, 1], c=blue_color, label=\"left\")\n",
    "plt.scatter(cones_right[:, 0], cones_right[:, 1], c=yellow_color, label=\"right\")\n",
    "plt.scatter(cones_unknown[:, 0], cones_unknown[:, 1], c=\"k\", label=\"unknown\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.plot(\n",
    "    [car_position[0], car_position[0] + car_direction[0]],\n",
    "    [car_position[1], car_position[1] + car_direction[1]],\n",
    "    c=\"k\",\n",
    ")\n",
    "plt.title(\"Computed path\")\n",
    "plt.plot(*path[:, 1:3].T)\n",
    "\n",
    "plt.axis(\"equal\")\n",
    "\n",
    "plt.show()\n",
    "\n",
    "plt.title(\"Curvature over distance\")\n",
    "plt.plot(path[:, 0], path[:, 3])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-1.5297177038177339,\n",
       " 11.507768392038084,\n",
       " -2.13906506809308,\n",
       " 10.026103145557148)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_cones = np.row_stack([cones_left, cones_right, cones_unknown])\n",
    "\n",
    "\n",
    "plt.plot(*all_cones.T, \"o\", c=\"k\")\n",
    "plt.plot(*sorted_left.T, \"o-\", c=blue_color)\n",
    "plt.plot(*sorted_right.T, \"o-\", c=yellow_color)\n",
    "plt.title(\"Sorted cones\")\n",
    "plt.axis(\"equal\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "plt.plot(*all_cones.T, \"o\", c=\"k\")\n",
    "plt.plot(*left_cones_with_virtual.T, \"o-\", c=blue_color)\n",
    "plt.plot(*right_cones_with_virtual.T, \"o-\", c=yellow_color)\n",
    "plt.title(\"Left and right cones with virtual cones\")\n",
    "plt.axis(\"equal\")\n",
    "plt.show()\n",
    "\n",
    "plt.plot(*all_cones.T, \"o\", c=\"k\")\n",
    "\n",
    "\n",
    "for left, right_idx in zip(left_cones_with_virtual, left_to_right_match):\n",
    "    plt.plot(\n",
    "        [left[0], right_cones_with_virtual[right_idx][0]],\n",
    "        [left[1], right_cones_with_virtual[right_idx][1]],\n",
    "        \"-\",\n",
    "        c=blue_color,\n",
    "    )\n",
    "\n",
    "\n",
    "for right, left_idx in zip(right_cones_with_virtual, right_to_left_match):\n",
    "    plt.plot(\n",
    "        [right[0], left_cones_with_virtual[left_idx][0]],\n",
    "        [right[1], left_cones_with_virtual[left_idx][1]],\n",
    "        \"-\",\n",
    "        c=yellow_color,\n",
    "        alpha=0.5,\n",
    "    )\n",
    "\n",
    "plt.title(\"Left and right matches\")\n",
    "plt.axis(\"equal\")\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.12 ('.venv': venv)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "fabab8c9137361cfedcdc113dd7cea69cf0d085c5b1aca4a55c9d43f8e867e4e"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
